The game started with the Ferns on top, having the better of the possession and, in the 12th minute, they had a chance to take the lead. The ball fell to Annalie Longo after a scramble in the box but her shot was blocked from close range.
In the 19th minute Wales had their own chance to go ahead. Natasha Harding cut inside from the right wing and fired across goal.
Further chances fell to Liz Anton and Meikayla Moore to test O'Sullivan in the Wales net but it ended goalless at the break.
The second half saw the Ferns continue to push for the opener, with Rebekah Stott firing just over the bar from a corner in the 55th minute.
As the second half unfolded, substitutes Betsy Hassett, Kate Taylor, Gabi Rennie, Grace Jale, Hand and, making her Ferns debut, Ally Green, were introduced to freshen things up.
At the death, Hand had the chance to win it. Jale's cross found the head of Hand but a brilliant save by the Welsh keeper tipped it over the bar.
The Ferns had the better of the match, with Wales looking to play more on the counter, but it ended 0-0.
Following the match, Klimkova highlighted the development of the team in the last couple of games, despite not being able to claim the win.
"The clean sheet is positive. I think we had some good moments in the game. But overall today's performance was a little bit lower versus our performance against Norway.
"But we know what we have done between those games. We travelled from Norway to here. We had only one day for recovery and one training session and then back to play this tough opposition.
"I could see from our girls a bit of fatigue so that kind of possession that we are building, that we want to improve, wasn't great today but our high press, our defending was very positive and we created a couple of chances that could have gone our way and then we would be very happy with today's game. Unfortunately we hit the cross bar and it didn't go in but this is football.
"So we keep believing that our time is coming. We are improving. Overall the tour is very successful."
